Finite Group Databasebeta

#127×C449 #28385228

order14368
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C449 · Schur multiplier (H2) = C22×C4

Aliases

direct product#127×C449

Subgroups

subgroupG/H
center, socleC22×C449C23
commutator, Frattini, cosocleC22C23×C449
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C449 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7184

Conjugacy classes & character table

6286 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#43271751, #43271800, #43272174, …
maximal subgroup of#331×C449, #353×C449, #453×C449, …
maximal normal subgroup of#331×C449, #353×C449, #453×C449, …
maximal quotient of#384×C449, #390×C449, #392×C449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14368, 34);